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Generalization of Runge-Kutta discontinuous Galerkin method to LWR traffic flow model with inhomogeneous road conditions. (English) Zbl 1067.65105
The paper presents an algorithm generalizing the Runge-Kutta discontinuous Galerkin finite element method applied to the scalar hyperbolic conservation equation with a spacially varying flux. The equation is known as the Lightill-Whitham-Richards (LWR) model which is considered with discontinuity terms here. The paper contributes in the redesign of a numerical flux and a limiter resulting in exactly steady flows and stationary discontinuities. The key idea for the design is that the time evolution would follow the characteristic direction. Numerical simulations involving two fluxes and two limiters are supplied.

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
90B20 Traffic problems in operations research
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
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